Temperature control systems and methods play a vital role in many manufacturing processes. Current state of the art methods of controlling temperature in manufacturing process employ temperature control algorithms such as Proportional, Integral, Derivative (PID) algorithms or fuzzy logic. The PID algorithm is well known in control theory, and uses the difference between the current measured temperature and the desired temperature (the error value) to determine the amount of power to apply to a heating circuit. As the name suggests, there are three terms in the PID calculation. The proportional term provides a contribution to the power proportional to the error value. The integral term provides a contribution to the power proportional to the integral (sum) of the error value over time. The derivative term provides a contribution to the power proportional to the differential (rate of change of) the error value.
When changing the desired temperature, the PID algorithm responds to the changing set point (desired temperature) by increasing the power (if ramping up to a higher set point) or decreasing the power (if ramping down to a lower set point). Typically when ramping to a higher temperature, the measured temperature will lag behind the set point, and then over shoot the desired temperature and oscillate before settling in to match it. This is depicted in FIG. 1.
Of additional importance is limiting the ramp rate to protect against negative thermal effects on the object or objects being heated due to excessive internal temperature gradients within the object. This is of particular concern in semiconductor wafer processing systems. Excessive heating of the edge of a wafer relative to its center can result in physical and/or chemical damage that could render the wafer unuseable or lead to early failure of semiconductor chips manufactured from the wafer.
When heating or cooling from one temperature to another within a semiconductor wafer processing system, such as a furnace, it is important to stabilize at the desired setpoint temperature in a minimum amount of time. Classically, a furnace will use a controlled linear ramp to go from one temperature setpoint to another. Although this provides continuous setpoint temperature values, the resulting ramp rate is not continuous as shown in FIG. 1. Rather, the ramp rate jumps from 0 to some value (the ramp rate), and then back to zero when the final setpoint is reached. The second derivative of the setpoint is the temperature acceleration, which must be infinite in order to instantaneously jump from 0 ramp rate to a non-zero value and back again. Real objects are incapable of the instantaneous and infinite “acceleration” in temperature ramp rate that is necessary to heat or cool under this idealized regimen. The result is a time delay after the start of heating before the object's actual temperature ramp rate achieves the desired ramp rate. A similar effect of “heating inertia” occurs as the temperature of the object approaches the final setpoint. When the furnace shuts off, the temperature ramp “deceleration rate” must be negative infinity to bring the ramp rate from a non-zero value back to zero. As a result, the object's temperature overshoots the setpoint and then oscillates above and below it before finally settling down to a stable temperature as depicted in FIG. 1.
The time delay or lag in the beginning of the ramp phase, overshooting of the desired setpoint, and temperature oscillations about the setpoint that are associated with prior art control methods as shown in FIG. 1 are undesirable in many applications when stable and precise temperature control is required. Accordingly an improved system and method of temperature control is needed.